16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.3.16

The Rational and Jordan Forms

Mathematics — Linear Algebra · nonsingular-matrices-square-root

Problem

Use the result of Exercise 15 to prove that if

c

is a non-zero complex number and

N

is a nilpotent complex matrix, then

(cI + N)

has a square root. Now use the Jordan form to prove that every non-singular complex

n \times n

matrix has a square root.